The Apology of Algebra

Posted on October 30, 2017 by the Editor

By Rodolfo Espinoza. Rodolfo is a student at Centro Regional de Educación de Encarnación. He also studies philosophy independently. He lives in Encarnación, Paraguay. Please read his article and leave your thoughts and comments below.

Why should we learn things like algebra? It is not uncommon to hear people say things about the putative uselessness of subjects such as math. If one is to apply the principle of charity and refrain oneself from asking what people think the house they live in was built with (or, for that matter, how the money some care so much about is managed), one could take them to mean that they are not useful for our own personal lives.

Lest I fall pray to the straw man fallacy, I state that I am deliberately going to extend Fran Lebowitz’s claim that “in real life, there is no such thing as algebra”, to stand for every discipline conceived as too abstract to be important or immediately useful; afterwards, I will evaluate the argument in favour of that position, as I have identified it, and present some possible objections to it.

Who, then, holds such notion? It is not just the usual opinion among the lazy or the uneducated, but even among some of the learned. One is not, of course, going to care about the neutrons that might go faster than the speed of light if one has to keep two jobs to feed one’s family; nor if one is too busy working to achieve things in the world as to care about changing one’s view of it; or, at the end, if one claims to know the answer to every question. The position that these people endorse consists of certain criteria by which they judge whether or not the evaluated thing is helpful, as well as a justification for why one should take what is considered as such; the first part may be said to be factual, for it implies whether or not something satisfies the criteria; the second part is normative for it is, naturally, prescribing a course of action in respect to the object of thought.

What are, the question follows, the factors they are taking into account? I perceive the main one to be a hedonic and a pragmatic evaluation, closely related to what in philosophy is called consequentialism: everything is judged as good or bad based on the consequences it brings about. So, they would say, learning math, physics, chemistry or epistemology, is useless because none helps us to be happy (or to pay our bills which, in turn, helps us to be happy).

Now, when Aristotle invented logic, could he have guessed the enormous implication it would have for our own era, after being reworked and amplified by others? What if he had said that, because it was simply an intellectual exercise, it was useless? Moreover, what would have happened to modern medicine if early biologists followed the view that studying a cell was not relevant at all?

Indeed, there is no way for us to see how far the seemingly trivial things may go. Science finds the questions as it looks for answers, and it opens up more possibilities as it explains what is already there, so one can never say with anticipation which path one should take, which path will be infertile.

So I need only look at my laptop and think about the electric energy that is flowing through it, caused by the study of people that did not ask whether it was a “useful” thing to do right back then or not, for they could have no idea of its uses. I need only think about the laptop more deeply, made possible by Boolean algebra, just as every other digital machine, to dismiss the argument.

Thus, we see not just the things that have a direct implication on our way of live, but also indirect things, like math, that have a great implication too; many sciences would be lost without it.

As to my argument that having all these things enabled by, most often, disinterested inquiry, is better than not having them, I can only ask the opponents to be consistent with their own positions, for it seems clear that those who reject the things they dismiss as futile usually do so to enjoy what they themselves allow for. On the other hand, if the objection was made that perhaps these investigations are indeed useful, but not as useful as, say, helping the poor, I would reply that we have no idea of the implications that the investigations can bring about (by their own consequentialism, it is better for some people to suffer than for all of us to die because of climatic changes and the like), and that they are committing an either/or fallacy, being the case that both things can be done at the same time.

Now that we have seen that the factual claim is not tenable, I can turn to the justification of the very criteria by virtue of which some people get to the conclusion above.

As I said earlier, a consequentialist notion is quickly recognized. To argue whether consequentialism is the “true” moral account, people would have to get right into the abstract discussions that they are trying to avoid; for, as I have stated, it can be inferred from Lebowitz’s quote that he and those who think as he does wouldn’t engage in such complex and detached-from-the-world matters as are theories of truth or theories of knowledge. Besides, I claim that a disinterested inquiry might not only lead to the best consequences, but that the very inquiring leads us, already, to the satisfaction they would bring about. What is a better way to live than to try to make sense of our world? Isn’t changing our idea of what is good or useful, constantly reassessing our place in the world, the most pleasurable of things? And while it is true that science might advance what we already think is good, as is the case of technology, it can also change what we think is bad, as is the case of many ethical discussions concerning non-human animals or our behaviour towards the environment.

Even saying that to try to answer the questions we all ask ourselves at one moment in our lives is pointless, alongside everything that helps us in doing so, is in itself an account that requires further questions.

At the end, to say that “in real life, there is no such thing as algebra” does not only entail our supposed knowledge of reality (which is in a sign of our lack of it), but also our knowledge of answers we might not even be able to find without this sort of activity. And as I have used algebra to mean more than algebra, but every other inquiry that seems to have no practical implication as well, I conclude, among other things, that we must learn it because, if we don’t, we will never be able to find the best reasons for having done so.